高校大学生分类管理中基于等价类的属性约简算法应用

Application of Attribute Reduction Algorithm Based on Equivalent Class in Classification Management of College Students

摘要: 本文针对高校大学生群体的特殊性，提出利用形式概念分析进行学生分类管理，为学生工作者提供有价值的参考依据。将属性特征与等价类的方法应用于属性约简，提出了属性约简的判定定理并予以证明；其次提出属性约简及输出算法，首次将属性约简算法应用于高校大学生分类管理，具体做法是：根据属性建立二叉树，调用前序、中序及后序遍历，得到相应序列，首先删掉一个属性，再将每个概念的内涵与剩余属性求交集，若求交集的结果均为单元素集，则该属性可约，否则跳过该属性，重复以上步骤，可以得到约简集；随后讨论了算法的时间复杂度，本文首次将约简集输出算法的时间复杂度降为多项式级。通过实例分析，对比了其它属性约简算法的运行效率和分类能力，证明本文提出的算法具有可行性和正确性。最后进行了总结并讨论了开放性问题。

Abstract: Based on the particularity of the college student group, this paper proposes to use formal concept analysis for classification management of students, which provides valuable reference for student workers. This paper applies characteristics of attribute and equivalent class to attribute reduction, puts forward judging theorems of attribute reduction with demonstration; secondly, proposes an algorithm of attribute reduction and output, applies this algorithm to classification management of college students for the first time. Specifications are as follows: first of all, establish a binary tree with attributes and obtain sequences of PreOrder, InOrder and PostOrder; delete an attribute; then perform intersection between the rest of attributes and each intent of concepts gradually, if each result contains single element, then this attribute can be removed, otherwise, skip this attribute, repeat the procedures above, consistent set can be obtained, reduction set which involves the minimum elements of consistent set can be output as well; subsequently, discusses the time complexity, this paper reduces the time complexity of reduction set output to polynomial level for the first time. Comparing with other algorithms on runtime and ability of classification, experi-mental results show that the proposed method approves feasibility and accuracy, in the end, draws a conclusion and discusses open issues.